The locus of the foot of perpendicular drawn from the centre of the ellipse x²+3y² =6 on any tangent to it is

• (x²-y²)² = 6x²+2y²

• (x²-y²)² = 6x² -2y²

• (x²+y²)² = 6x²+2y²

• (x²+y²)² = 6x²+2y²

The slope of the line touching both the parabolas y² = 4x and x²-32y is 

• 1/2

• 3/2

• 1/8

• 1/8

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

• (-5,2)

• (2,-5)

• (5,-2)

• (5,-2)

The equation of the circle passing through the foci of the ellipse  and having centre at (0,3) is 

• x²+y²-6y-7 =0

• x²+y²-6y+7 =0

• x²+y²-6y-5 =0

• x²+y²-6y-5 =0

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 − T_n = 10, then the value of n is

• 7

• 5

• 10

• 10

Given A circle, 2x² + 2y²= 5 and parabola,  
Statement I An equation of a common tangent to these curves is 
Statement II If the line  is the common tangent, then m satisfies m⁴-3m²+2 =0

• Statement I is true,  Statement II is true; Statement II is a correct explanation for statement I

• Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I

• Statement I is true, Statement II is false

• Statement I is true, Statement II is false

Statement I An equation of a common tangent to the parabola  and the ellipse 2x² +y² =4 is .
Statement II If the line  is a common tangent to the parabola  and the ellipse 2x² +y² =4, then m satisfies m⁴ +2m² =24

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

8.

The area bounded between the parabolas x²=y/4 and x² = 9y, and the straight line y = 2 is

• 
• 
• 
• 

If z ≠ 1 and  is real, then the point represented by the complex number z lies

• either on the real axis or on a circle passing through the origin

• on a circle with centre at the origin

• either on the real axis or on a circle not passing through the origin

• either on the real axis or on a circle not passing through the origin

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

• 10/3

• 3/5

• 6/5

• 6/5